The bug report for the bug this mod fixes has been marked as resolved as of Minecraft 1.20.1-1.21.6.1.x.
This mod will continue to be updated and has a 1.20.1-1.21.6.1.x version, however as of Minecraft 1.20.1-1.21.6.1.x it is strongly recommended to use the vanilla Minecraft way of adding custom discs, which is through datapacks.
If you still wish to listen to custom discs through just the use of a resource pack though, you will need this mod. As of 1.20.1-1.21.6.1.x this mod now fixes the bug client-side as well, meaning you can join every server with a custom disc resource pack, without the disc being cut off.
README